Dynamic Graph Algorithms

Associated People:

Bruce Kapron (University of Victoria)

Valerie King (University of Victoria)

Ben Mountjoy (University of Victoria)

Associated Sites:

PIMS University of Victoria

Graphs are an abstract model of nodes and edges (links) between nodes and are used to model connections in such diverse areas as communications networks, protein networks, dependencies in databases and software, and social relationships. `Solving problems about large graphs can be computationally expensive, as the number of operations required may be proportional to the size of the graph, or even worse, the square or cube of its size. In the current world of streaming data, we are often considering not just a one-time graph problem, but an on-going problem, where the input is changing over time as links are being added and removed or nodes are turning on and off. The goal of dynamic graph algorithms is to maintain solutions while processing updates very quickly.

The problem of graph connectivity is to determine for any pair of nodes if they are connected by a path. Dr. Bruce Kapron, Dr. Valerie King, and her master's student Ben Mountjoy recently discovered a new randomized technique for monitoring graph connectivity in a dynamic graph, which greatly reduces the time needed to process any individual update. The new technique relies on a novel way of compressing information about randomly sampled edges in the graph. This work won best paper in the ACM-SIAM Symposium on Discrete Algorithms (2013).